PHOENIX -- An Arizona congressman urged the Obama administration not to cooperate when illegal immigrants are picked up by local police if a tough new state immigration law survives legal challenges.

U.S. Rep. Raul Grijalva, a Democrat, and civil rights activists spoke on Sunday to thousands of people gathered at the state Capitol and called on President Barack Obama to fight the law, promising to march in the streets and invite arrest by refusing to comply.

"We're going to overturn this unjust and racist law, and then we're going to overturn the power structure that created this unjust, racist law," Grijalva said.

Obama has called the new law "misguided" and instructed the Justice Department to examine it to see if it's legal. It requires police to question people about their immigration status -- including asking for identification -- if they suspect someone is in the country illegally. Opponents say it would lead to racial profiling because officers would be more likely to ask people who look Hispanic.

Supporters have dismissed concerns about profiling, saying the law prohibits the use of race or nationality as the sole basis for an immigration check. Gov. Jan Brewer, who signed the measure Friday, has ordered state officials to develop a training course for officers to learn what constitutes reasonable suspicion someone is in the U.S. illegally.

State Sen. Russell Pearce, the Mesa Republican who sponsored the legislation, said it's "pretty disappointing" that opponents would call on the federal government to refuse to cooperate with Arizona authorities.

"It's outrageous that these people continue to support law breakers over law keepers," Pearce said Sunday.

Protesters, some of whom came from as far away as Texas, clustered under trees for shelter from Arizona's searing sun and temperatures that approached 90 degrees. Police said it was peaceful and there were no clashes.

Bill Baker, 60, took time off work at a downtown Phoenix restaurant to sell umbrellas and Mexican and American flags to the largely Hispanic crowd. He said he wasn't making much money, but he wanted to help them exercise their freedom of expression -- even though he supports the law they all showed up to oppose.

"If I go to another foreign country, if I go to Mexico, I have to have papers," Baker said. "So I don't feel there's anything particularly harsh about the law."

He said he's worried the bill will hurt the economy if many of Arizona's estimated 460,000 illegal immigrants leave the state and stop spending money here.

"But that's the price you have to pay to have a lawful country," Baker said.

Current law in Arizona and most states doesn't require police to ask about the immigration status of those they encounter, and many police departments prohibit officers from inquiring out of fear immigrants won't cooperate in other investigations.

The new law makes it a crime under state law to be in the country illegally. Immigrants unable to produce documents showing they are allowed to be in the U.S. could be arrested, jailed for up to six months and fined $2,500. Other provisions allow lawsuits against government agencies that hinder enforcement of immigration laws, and the law makes it illegal to hire illegal immigrants for day labor or knowingly transport them.

Arizona officers would arrest people found to be undocumented and turn them over to federal immigration officers. Opponents said the federal government can block the law by refusing to accept them.

"Our message today is: 'Mr. President we listened, and we came out in record massive numbers to support you,"' said U.S. Rep. Luis Gutierrez, D-Ill. "We need you to support us today."

Gutierrez is one of the nation's loudest voices calling for comprehensive immigration reform that would create a pathway to citizenship for the millions of illegal immigrants now in the United States. He called on Obama to live up to a campaign promise to pass immigration reform.

The Rev. Al Sharpton, speaking Sunday in New York, said that just as freedom riders battled segregation in the 1960s, he would organize "freedom walkers" to challenge the Arizona bill.

"We will go to Arizona when this bill goes into effect and walk the streets with people who refuse to give identification and force arrest," Sharpton said.

Arizona's border with Mexico is the nation's busiest stretch for illegal border crossings. The state's harsh, remote desert serves as the gateway to the U.S. for thousands of Mexicans and Central Americans.

"It divides our whole community," said Mary Hoffmann, 54, a landscape architect in Phoenix. "If people are divided they make decisions on fear and anger."

Brewer, who faces a tough re-election battle and growing anger in the state over illegal immigrants, said the law "protects every Arizona citizen" and the state must act because the federal government has failed. Brewer said she wouldn't tolerate racial profiling.

The March 27 shooting death of rancher Rob Krentz on his property in southeastern Arizona brought illegal immigration and border security into greater focus in the state. Authorities believe Krentz was killed by an illegal border crosser.

Since the shooting, Brewer and other officeholders and candidates have toured the state's border with Mexico. She has ordered a reallocation of state National Guard and law enforcement resources and called on the federal government to deploy National Guard troops.